Fifth Grade Math - Multiply Whole Numbers by 3-Digit Numbers

Understanding multiplication with 3-digit numbers

Multiplication is a mathematical operation that combines equal groups. When multiplying by 3-digit numbers, we're finding the total when we have hundreds, tens, and ones groups of a certain amount.

Example:

324 × 5 means 5 groups of 324
156 × 23 means 23 groups of 156

Remember

Multiplication is repeated addition. 4 × 325 is the same as 325 + 325 + 325 + 325.

The Standard algorithm for 3-digit multiplication

The standard algorithm is a step-by-step method for multiplying larger numbers. We multiply each digit of one number by each digit of the other number, carefully considering place value.

Steps for 324 × 156:

Step 1: Multiply 324 × 6 (ones place)
Step 2: Multiply 324 × 50 (tens place)
Step 3: Multiply 324 × 100 (hundreds place)
Step 4: Add all partial products

Important

Always align numbers by place value. Use zero as a placeholder when moving to the next place value.

Breaking down the process

To solve 3-digit multiplication problems, we use the partial products method. This means we multiply each part of one number by the other, then add all the partial products together to find the total.

Example: 324 × 156

Multiply 324 by the ones digit (6): 324 × 6 = 1,944
Multiply 324 by the tens digit (5 → 50): 324 × 50 = 16,200
Multiply 324 by the hundreds digit (1 → 100): 324 × 100 = 32,400
Add the partial products: 1,944 + 16,200 + 32,400 = 50,544

              324
            × 156
            —————
            1,944   ← 324 × 6
           16,200   ← 324 × 50
         + 32,400   ← 324 × 100
        ——————————
           50,544

Tip

Each new place value adds a zero: multiply by tens → add one zero, multiply by hundreds → add two zeros. Then, add all partial products to get the final answer.

Regrouping in multiplication

Regrouping (also called carrying) happens when a product in one place value is 10 or more. The extra value is moved, or “carried,” to the next higher place value.

Example: 487 × 36 (with regrouping)

We’ll multiply step by step using the standard algorithm.

Step 1: Multiply 487 by the ones digit (6).

6 × 7 = 42 → write 2, carry 4.
6 × 8 = 48, plus the carried 4 = 52 → write 2, carry 5.
6 × 4 = 24, plus the carried 5 = 29 → write 29.
Partial product = 2,922

Step 2: Multiply 487 by the tens digit (3, which means 30).

3 × 7 = 21 → write 1, carry 2.
3 × 8 = 24, plus the carried 2 = 26 → write 6, carry 2.
3 × 4 = 12, plus the carried 2 = 14.
Because we’re multiplying by 30 (not 3), add one zero at the end.
Partial product = 14,610

Step 3: Add the partial products.

2,922 + 14,610 = 17,532

              487
            ×  36
            —————
            2,922   ← 487 × 6
         + 14,610   ← 487 × 30
        —————————
           17,532

Remember

When a product is 10 or greater, carry the tens digit to the next column. Always add the carried value to your next multiplication result.

Checking your work

It's important to verify your multiplication results. You can use estimation or reverse operations to check if your answer is reasonable.

Ways to check:

Estimation: 324 × 156 ≈ 300 × 160 = 48,000
Division: 50,544 ÷ 324 should equal 156
Repeat the calculation

Good Habit

Always estimate first to know approximately what your answer should be. This helps catch major errors.

Real-world applications

Multiplying by 3-digit numbers has many practical uses in everyday life and future math concepts.

Real situations:

Calculating total costs: 125 items at $3.45 each
Finding area: A room that is 345 cm by 280 cm
Determining distance: 365 days of walking 2.5 miles each day

Connection

This skill prepares you for more advanced math including decimals, fractions, and algebra.

Go to the practice →